Answer to Question #704 in Mechanics | Relativity for Brian

Question

For the intercontinental ballistic missile to have a range of 6000 km, what must be the speed v0 of the missile at the end of the accelaration phase?

Answer 1

We know that maximal range is achieved when the angle of projection is equal to 45°.

Range, R = vo² * sin2α ÷ g ,

v0 = √ R*g ÷ sin2α =

√ 6000 km * 9.8 * 0.001 km/s² ÷ sin(2 * 45°) = 7.668 km/s